Magnetic resonance imaging is now used as one of important medical modalities in a medical center. A system for executing this magnetic resonance imaging is called a magnetic resonance imaging device. A high frequency magnetic field is applied to the imaged body, and the magnetic resonance phenomenon is generated in a magnetized spin within the imaged body. An echo signal generated by this magnetic resonance phenomenon is collected. Such operations are executed as a time series. An MR image of the imaged body is basically obtained by processing this echo signal (including reconstruction processing). Such a series of operations is called a scan.
In magnetic resonance imaging, it is preferable that the imaged body not move (including body movement due to heart beating and respiratory breathing) during this scan. Such a movement becomes a motion artifact and deteriorates the quality of the reconstructed MR image. Therefore, restraint of motion artifact is an important technical theme in magnetic resonance imaging.
A method using an magnetic gradient (inclining) field pulse called a navigator is known as one of methods for restraining the motion artifact when magnetic resonance imaging is performed by using a pulse sequence of a multi-shot type. In this method, movement of the imaged body is monitored by using the echo signal (also called the navigator echo signal, or briefly called the navi echo) collected by applying this navigator, and the collecting data are corrected on the basis of this monitor information (see non-patent literature references 1-8).
As can be seen from non-patent literature references 1 and 2, the mode of data for monitoring the movement was first a one-dimensional projecting profile. In contrast to this, recently, as can be seen from non-patent literature references 4, 5 and 7, a system for two-dimensionally monitoring and correcting the movement during the scan is also proposed.
However, in the methods reported so far, a rigid movement of a head portion, etc., i.e., parallel translation and a rotating movement as a rigid body are set to objects. With respect to a movement having a spatial distribution in the movement, i.e., a non-rigid movement, a movement collected within a voxel as in diffusion imaging is set to an object (see non-patent literature reference 7). It is merely reported in application (see patent literature reference 9) able to separate a movement component in a time series image of the head portion at a spatial frequency. However, it is not reported in a structure in which the non-rigid movement for spatially non-uniformly moving (shifting) each position forming the abdominal part as in the movement (motion) of a breathing property of the abdominal part, etc. is set to an object.
The technical reasons for this lack of report will be explained. When the rigid body is shifted in a linear position in a direction parallel with this inclining magnetic field under an inclining magnetic field of constant intensity and constant time in the magnetic resonance imaging, this position shift is proportional to a shift amount of an average phase in the r(real)-space (exactly, it is also called a hybrid space (h-space) since it is the r-space on only one side axis and is the k-space on the other axis). Accordingly, when the shift is non-linear every position, i.e., the shift amount every position is different, it is impossible to know the spatial distribution of the movement even when the average phase is calculated.
On the one hand, the non-linear movement can be corrected if the spatial distribution of the position shift caused by the movement can be measured in accordance with a changing frequency. It is necessary to newly apply a navigator pulse every shot as well as the pulse sequence for imaging so as to measure the movement. However, in the case of this technique, time-like restriction is added to the navi echo collected to calculate a two-dimensional distribution of the movement. On the other hand, since it is comparatively easy to measure the movement as one dimension as projection data of a certain axis direction, there are many reports. However, the application of this technique is limited to the linear movement as the rigid body, and it is difficult to cope with the non-linear movement.
The case for measuring the navi echo as the one-dimensional projection data will be described in detail. In this case, normally, in addition to the echo for imaging, the navi echo of a read-out direction provided when a phase encode amount is set to zero every shot and the navi echo is collected while applying the inclining magnetic field in the read-out direction of the imaging, i.e., projection data in the phase encode direction are acquired and corrected. In this case, with respect to the navi echo of the read-out direction, the projection data integrated along the phase encode direction can be acquired with respect to each position of the read-out direction in timing considered to make the same movement as the collecting time of the echo for imaging. Therefore, the echo for imaging can be corrected correspondingly to each line of each projection data in the read-out direction. Accordingly, it is also possible to cope with the non-linear movement in the read-out direction to a certain extent (see non-patent literature reference 1).
However, in the case of navi echo collection of the read-out direction at imaging time, the non-linear correction with respect to the movement in the phase encode direction is impossible. Accordingly, the navi echo of the phase encode direction is used. However, in this case, differing from the navi echo of the read-out direction, the echo data for imaging acquired in the same moving state as the navi echo are data on only a line acquired in the same shot as the navi echo. Therefore, in the phase encode direction of the echo for imaging, data acquired in the moving state different for every shot are mixed. Therefore, even when these data are corrected to data of the r-space (also called the hybrid-space (h space)) by performing Fourier transform in the phase encode direction as they are, it does not correspond to the line of the navi echo Fourier-transformed. Accordingly, it is difficult to make the non-linear movement correction of the phase encode direction by the navi echo of the phase encode direction. However, in this case, the correction can be also made if zero is put close to a position except for the shot corresponding to the navi echo in the k-space of the echo for imaging, and the data transformed to the hybrid space (h-space) are corrected every shot and are synthesized.
Thus, it is possible to measure the shift of the position due to a spatially non-uniform movement and the distribution of the phase in principle, and make the correction in the r-space every voxel. However, a measuring technique (a pulse sequence or an external monitor) of the movement different from the original imaging technique (pulse sequence) is required. Accordingly, it is difficult to make the measurement itself in time and technique. In addition to this, it is necessary to execute the measurement and the correction by a shot number with respect to one image. Therefore, as the number of shots is increased, an arithmetic amount becomes enormous and nonrealistic. In a case using a one-dimensional distribution as projection, the movement of the read-out direction of imaging can be also made in non-linearity by measuring the position shift every projection line in the r-space and reversely performing the shift, but the arithmetic amount is increased. When the non-linear movement of the phase encode direction of imaging is set to an object, the arithmetic amount is further increased. In this case, no interpolation is required in the correction in the k-space. However, in the correction in the real space, the interpolation is required in the correction of the shift in a degree of 1 pixel or less.
This situation will be described in detail with the spin warp method of the multi-shot as an example. In the case of the spin warp method of the multi-shot; collective data of a certain line number are acquired by performing division in the phase encode direction in the k-space every one shot. Therefore, data influenced by the movement different every shot are mixed in the k-space. In the non-linear correction of the spatial positions, turning-back is caused in the image space even when a distribution ΔY(y,n) of the non-linear shift every position y is measured in the r-space every shot, and the corrected image is repeatedly made. Therefore, portions of different movements are overlapped and cannot be distinguished so that no correction can be made in principle. With respect to the measurement itself, in the case of the non-linear movement, it is very difficult to identify the position relation before and after the movement of the same portion every voxel. In particular, in the case of the normal spin warp method, data every one line are collected every shot and are converted into data of the r-space every line, and the shift amount every position y is then measured. Thereafter, the position correction is made every position y. Accordingly, the arithmetic amount becomes enormous in both the measurement and the correction.
On the other hand, in k-space, the measurement and the correction can be easily made until the phase distributions of spatial zeroeth and first orders. The position shift in r-space becomes a phase shift in k-space. Therefore, it is sufficient to arithmetically calculate the product of a phase term at the same point of k-space, and the correction of a sub-pixel or less in r space can be also made. Therefore, the arithmetic calculation in k-space is desirable in consideration of convenience of processing. However, in k-space, it is limited to measurement and correction of linear motion, and measurement and correction of spatial non-linear motion are difficult.                Patent literature reference 1: Ehman R L, Felmlee, J P. Radiology. Adaptive technique for high-definition MR imaging of moving structures. Radiology 1989 October; 173(1): 255-63. Non-patent literature reference 2: Ordidge R J, Helpern J A, Qing Z X, Knight R A, Nagesh V. Correction of motional artifacts in diffusion-weighted MR images using navigator echoes. Magn Reson Imaging. 1994; 12(3): 455-60. Non-patent literature reference 3: Wang Y, Rossman P J, Grimm R C, Riederer S J, Ehman R L, Navigator-echo-based real-time respiratory gating and triggering for reduction of respiration effects in three-dimensional coronary MR angiography. Radiology. 1996 January; 198(1): 55-60. Non-patent literature reference 4: Pipe J G. Motion correction with PROPELLER MRI: application to head motion and free-breathing cardiac imaging. Magn Reson Med. 1999 November; 42(5): 963-9. Non-patent literature reference 5: Pipe J G, Farthing V G, Forbes K P. Multishot diffusion-weighted FSE using PROPELLER MRI. Magn Reson Med 2002 March; 47(3): 621. Non-patent literature reference 6: McGee K P, Grimm R C, Felmlee J P. Rydberg J R, Riederer S J, Ehman R L. The shoulder: adaptive motion correction. Radiology. 1997 November; 205(2): 541-5. Non-patent literature reference 7: Miller K L, Pauly J M. Non-linear phase correction for navigated diffusion imaging. Magn Reson Med. 2003 August; 50(2): 343-53. Non-patent literature reference 8: Manke D, Nehrke K, Bornert P. Novel prospective respiratory motion correction approach for free-breathing coronary MR angiography using a patient-adapted affine motion model. Magn Reson Med. 2003 July; 50(1): 122-31. Non-patent literature reference 9: Langenberger K W, Moser E. Non-linear motion artifact reduction in event-triggered gradient-echo FMRI. Magn Reson Imaging. 1997; 15(2): 163-7.        